Study on Key Biological Indicators of Diabetes Based on Statistical Tests

Normality testing is a fundamental hypothesis test in the statistical analysis of key biological indicators of diabetes.If this assumption is violated,it may cause the test results to deviate from the true value,leading to incorrect inferences and conclusions,and ultimately affecting the validity and accuracy of statistical inferences.Considering this,the study designs a unified analysis scheme for different data types based on parametric statistical test methods and non-parametric test methods.The data were grouped according to sample type and divided into discrete data and continuous data.To account for differences among subgroups,the conventional chi-squared test was used for discrete data.The normal distribution is the basis of many statistical methods;if the data does not follow a normal distribution,many statistical methods will fail or produce incorrect results.Therefore,before data analysis and modeling,the data were divided into normal and non-normal groups through normality testing.For normally distributed data,parametric statistical methods were used to judge the differences between groups.For non-normal data,non-parametric tests were employed to improve the accuracy of the analysis.Statistically significant indicators were retained according to the significance index P-value of the statistical test or corresponding statistics.These indicators were then combined with relevant medical background to further explore the etiology leading to the occurrence or transformation of diabetes status.

Analysis of College Students’ Test Scores Based on Two-Component Mixed Generalized Normal Distribution

In order to improve the fitting accuracy of college students’ test scores, this paper proposes two-component mixed generalized normal distribution, uses maximum likelihood estimation method and Expectation Conditional Maxinnization (ECM) algorithm to estimate parameters and conduct numerical simulation, and performs fitting analysis on the test scores of Linear Algebra and Advanced Mathematics of F University. The empirical results show that the two-component mixed generalized normal distribution is better than the commonly used two-component mixed normal distribution in fitting college students’ test data, and has good application value.

Applications of Normality Test in Statistical Analysis

In this study, to power comparison test, different univariate normality testing procedures are compared by using new algorithm. Different univariate and multivariate test are also analyzed here. And also review efficient algorithm for calculating the size corrected power of the test which can be used to compare the efficiency of the test. Also to test the randomness of generated random numbers. For this purpose, 1000 data sets with combinations of sample size n = 10, 20, 25, 30, 40, 50, 100, 200, 300 were generated from uniform distribution and tested by using different tests for randomness. The assessment of normality using statistical tests is sensitive to the sample size. Observed that with the increase of n, overall powers are increased but Shapiro Wilk (SW) test, Shapiro Francia (SF) test and Andeson Darling (AD) test are the most powerful test among other tests. Cramer-Von-Mises (CVM) test performs better than Pearson chi-square, Lilliefors test has better power than Jarque Bera (JB) Test. Jarque Bera (JB) Test is less powerful test among other tests.

Testing for Normality from the Parametric Seven-Number Summary

The objective of this study is to propose the Parametric Seven-Number Summary (PSNS) as a significance test for normality and to verify its accuracy and power in comparison with two well-known tests, such as Royston’s W test and D’Agostino-Belanger-D’Agostino K-squared test. An experiment with 384 conditions was simulated. The conditions were generated by crossing 24 sample sizes and 16 types of continuous distributions: one normal and 15 non-normal. The percentage of success in maintaining the null hypothesis of normality against normal samples and in rejecting the null hypothesis against non-normal samples (accuracy) was calculated. In addition, the type II error against normal samples and the statistical power against normal samples were computed. Comparisons of percentage and means were performed using Cochran’s Q-test, Friedman’s test, and repeated measures analysis of variance. With sample sizes of 150 or greater, high accuracy and mean power or type II error (≥0.70 and ≥0.80, respectively) were achieved. All three normality tests were similarly accurate;however, the PSNS-based test showed lower mean power than K-squared and W tests, especially against non-normal samples of symmetrical-platykurtic distributions, such as the uniform, semicircle, and arcsine distributions. It is concluded that the PSNS-based omnibus test is accurate and powerful for testing normality with samples of at least 150 observations.

Wigner-Matrix-Based Normality Test and Application to Weak Signal Detection in SISO/SIMO Systems

Based on the asymptotic spectral distribution of Wigner matrices, a new normality test method is proposed via reforming the white noise sequence. In this work, the asymptotic cumulative distribution function （CDF） of eigenvalues of the Wigner matrix is deduced. A numerical Kullback-Leibler divergence of the empiric-d spectral CDF based on test samples from the deduced asymptotic CDF is established, which is treated as the test statistic. For validating the superiority of our proposed normality test, we apply the method to weak SIPSK signal detection in the single-input single-output （SISO） system and the single-input multiple-output （SIMO） system. By comparing with other common normality tests and the existing signal detection methods, simulation results show that the proposed method is superior and robust.

A note on self-normalized Dickey-Fuller test for unit root in autoregressive time series with GARCH errors

In this article, the unit root test for AR（p） model with GARCH errors is considered. The Dickey-Fuller test statistics are rewritten in the form of self-normalized sums, and the asymptotic distribution of the test statistics is derived under the weak conditions.

Test of Normality of Waist Measurement Data of Young Male and Female Adults based on the Quantile - Quantile Plot

This paper investigates the normality of some real data set obtained from waist measurements of a group of 49 young adults. The quantile - quantile （Q-Q） plot and the analysis of correlation coefficients for the Q-Q plot is used to determine the normality or otherwise of the data set. In this regards, the probabilities of the quantiles were computed, modified and plotted. Thereafter the correlation coefficients for the quantile - quantile plots were obtained. Results indicate that at 0.1 level of significance, the data for young adult males of the sample were not normally distributed, and had a mean value that is within the range of low risk, healthwise, whereas the distribution of the data for young female adults showed reasonable normality, but also with a mean value that is within the range of low risk in terms of health condition.

Constant-Step Stress Accelerated Life Test of VFD under Logarithmic Normal Distribution Case

In order to solve the life problem of vacuum fluorescent display (VFD) within shorter time, and reduce the life prediction cost, a constant-step stress accelerated life test was performed with its cathode temperature increased. Statistical analysis was done by applying logarithmic normal distribution for describing the life, and least square method (LSM) for estimating logarithmic normal parameters. Self-designed special software was used to predict the VFD life. It is verified by numerical results that the VFD life follows logarithmic normal distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. The accurate calculation of the key parameters enables the rapid estimation of VFD life.

The Normal Color Vision Evaluated With FM 100-hue Test

One hundred and twenty normal subjects (240 eyes) agedfrom 10 to 69 were tested with FM 100-hue test.They were divided into6 groups according to their age.It was shown that there were no statisti-cally significant difference in the total error score (TES) between the malesand females or between the right and left eyes,but there existed some rela-tionships between the TES and age.The total error score (TES) was thelowest in the 20-29 age group and increased gradually with aging.Theanalysis of the partial...

On Rotational Robustness of Shapiro-Wilk Type Tests for Multivariate Normality

The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.

二项分布双边收尾概率和假设检验统计量的几处修正

二项分布是广泛存在的一种离散型概率分布。服从二项分布B(n,p)的一个随机变量等于n个相互独立且服从贝努利分布B(1,p)的随机变量之和,二项分布包含参数p的估计与检验等同于贝努利分布参数p的估计与检验。本文修正常见教科书中有关二项分布双边收尾概率计算和假设检验统计量构建中存在的3处问题。(1)对二项分布B(n,p)的取值概率pk(k=0,1,…,n)从小到大排序,排序后的概率用p_((k))表示,观测值k的双边收尾精确概率等于■;(2)二项分布B(n,p)参数p与给定值p0的差异显著性检验统计量被修正为■,该统计量在大样本条件下近似服从正态分布N(p–p0,1);(3)二项分布B(n1,p1)和B(n2,p2)的参数p1和p2差异显著性检验统计量被修正为■,该统计量在大样本条件下近似服从正态分布N(p1–p2,1)。修正后的双边收尾概率是精确值,不会出现概率大于1的问题。修正后的2个检验统计量无论原假设是否成立,其大样本近似正态分布的方差均为1,有利于准确研究备择假设条件下检验统计量的功效。此外,文中还介绍了小样本条件下二项分布参数的精确检验,对比分析了准确检验与近似检验的异同;讨论了修正统计量的理论基础,给出了小概率和大样本的判定标准,列出了贝努利分布参数检验与正态分布均值检验的异同。期望读者能够从中了解到假设检验与统计推断作为统计学核心研究内容的全貌。

A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.

A Comprehensive Guide for Selecting Appropriate Statistical Tests: Understanding When to Use Parametric and Nonparametric Tests

Choosing appropriate statistical tests is crucial but deciding which tests to use can be challenging. Different tests suit different types of data and research questions, so it is important to choose the right one. Knowing how to select an appropriate test can lead to more accurate results. Invalid results and misleading conclusions may be drawn from a study if an incorrect statistical test is used. Therefore, to avoid these it is essential to understand the nature of the data, the research question, and the assumptions of the tests before selecting one. This is because there are a wide variety of tests available. This paper provides a step-by-step approach to selecting the right statistical test for any study, with an explanation of when it is appropriate to use it and relevant examples of each statistical test. Furthermore, this guide provides a comprehensive overview of the assumptions of each test and what to do if these assumptions are violated.

软土地层盾构掘进参数分析及掘进速度预测

依托佛山地铁3号线逢沙站—创意园站区间隧道工程,通过现场实测数据,详细分析了土压平衡盾构穿越软土地层时盾构掘进参数内在变化规律,并建立了掘进速度预测模型。首先,对盾构掘进参数进行数理统计分析,对各掘进参数的分布进行正态性检验;其次,进行Pearson相关性分析,找出线性相关性较强参数间变化规律;再次,利用基于互信息的特征选择算法,筛选与掘进速度非线性相关性较高的参数变量;最后,分别建立随机森林回归预测模型和基于遗传算法优化BP神经网络预测模型,对掘进速度进行预测。研究结果表明:在软弱地层盾构隧道工程中,通常采用较低的刀盘转速、刀盘扭矩及较高的掘进速度、贯入度、盾构总推力、土仓压力;掘进速度等参数均通过了采用K-S检验法的正态性检验;掘进速度与贯入度存在极强相关性关系;基于遗传算法优化BP神经网络预测模型的预测精度略优于随机森林回归预测模型,随机森林回归预测模型在测试集中的平均绝对误差、均方根误差、拟合优度分别为4.055、5.038、0.871,而基于遗传算法优化BP神经网络预测模型分别为0.822、1.244、0.991。

正断层错动作用下矿山法隧道受力变形机理的模型试验研究

为研究正断层错动作用下矿山法隧道的受力变形机理,以胶州湾第二海底隧道穿越沧口断裂为工程背景,采用自研的大比尺穿越断层隧道结构破坏加载试验装置,针对设置柔性连接变形缝和变形缝间距对隧道结构抗错断效果的影响,开展几何相似比为1∶40的矿山法隧道穿越倾角70°的正断层错动模型试验,对错动试验过程中的隧道变形、应变分布、围岩接触压力和破坏特性等关键指标进行监测,分析获得了正断层错动作用下隧道变形和力学响应规律。研究结果表明:(1)隧道在正断层错动作用下,呈现纵向拉弯+竖向挤压的受荷模式,在下盘邻近断层面处拱顶部位和上盘邻近断层面处仰拱部位出现脱空区;(2)隧道开裂主要以纵向贯通裂缝为主,近断层面处衬砌还出现了部分斜向裂缝和环向裂缝;(3)节段间的连接形式和节段长度不会根本上改变隧道在断层错动作用下的受荷模式和变形模式,但节段间刚度越小,节段长度越小,结构对于地层强制位错的适应性就更好;(4)相比于刚性连接,节段间的柔性连接吸收了大部分地层强制位错,有效降低衬砌节段的荷载和变形,使结构趋于安全。

引入相量算子和流向算子的天鹰优化算法

针对天鹰优化算法搜索效率不足,容易陷入局部最优的缺点,提出多策略改进天鹰优化算法(MIAO).引入广义正态分布优化算法(GNDO),将该算法得出的结果与天鹰优化算法第1阶段得出的结果进行比较,筛选出这2种优化算法下的最优值.该操作扩大了搜索空间,提高了解的质量.引入相量算子,将第2阶段变为自适应的非参数优化,提高算法的高维优化能力.针对天鹰优化算法在迭代后期存在种群多样性降低、局部开发能力不足的问题,在天鹰算法的第3阶段引入流向算子,使信息可以在每个个体间相互传递,提高种群信息的利用率,增强天鹰优化算法的开发性能.通过对16个测试函数寻优对比分析以及Wilcoxon秩和检验可知,MIAO的寻优能力和收敛速度都有较大的提升.为了验证MIAO算法的实用性和可行性,采用所提算法求解减速器设计问题,通过实际工程优化问题的实验对比分析可知,MIAO算法在处理现实优化问题上具有一定的优越性.

多策略融合的改进哈里斯鹰算法及其路径规划应用

针对哈里斯鹰算法(HHO)后期缺乏全局搜索、易陷入局部极值等问题,提出了一种多策略融合的改进哈里斯鹰算法(MFHHO).首先,提出了自适应混沌和核心种群划分策略,平衡算法后期的全局和局部搜索性能,提高算法的多样性;其次,修改位置更新公式,将莱维飞行替换为黄金正弦策略,提高算法寻优性能和效率;最后,融合自适应正态云最优解扰动策略,提高算法跳出局部最优解的能力.在国际测试函数、CEC2014复杂函数的数值实验中,改进算法性能提升明显;在路径规划实验中,改进算法性能最优,相较于对照组算法性能提升了14.75%,且具有较好的稳定性.

食品检测中近红外光谱分析技术的应用研究

为了实现对食品成分、品质等方面的准确检测,为食品安全监管和质量控制提供有效的技术支持,引入近红外光谱分析技术,开展了该项技术在食品检测中的应用研究。通过样品制备、选择光谱采集设备、设置采集参数,采集食品近红外光谱,引入标准正态变量变换算法和自适应滤波算法,预处理采集的光谱数据,基于预处理后的数据,结合主成分分析法,构建食品成分特征与近红外光谱数据之间的数学模型,实现近红外光谱分析技术在食品检测的应用设计。实验结果表明,提出的研究应用后,食品成分检测结果与真实值更加接近,检测均方根误差较小,食品检测的准确性得到了显著提升。

土工格室加筋正常固结粉质黏土应力应变响应

土工格室加筋正常固结粉质黏土对工程建设意义重大。基于土工格室与填土的相互作用机制和增量法,采用弹塑性理论、邓肯-张双曲线模型、修正剑桥屈服函数以及剪胀方程,推导了土工格室加筋正常固结黏土的应力应变响应计算模型,进行了土工格室加筋正常固结黏土的三轴固结排水剪切试验,实测不同围压下的应力应变关系,采用三轴试验结果验证了所提理论模型的正确性和可靠性。此外,采用所提理论模型进行了参数敏感分析,研究了填土的力学性质参数、格室的网格尺寸和力学性质参数对于加筋土应力应变响应的影响。研究结论表明,与砂砾料相似,土工格室约束作用对于正常固结黏土的内摩擦角影响较小,而黏聚力有所增加;随着轴向应变的增加或围压的减小,加筋效果逐渐明显;加筋正常固结黏土的强度和刚度随着非线性弹性常数k的增加、强度参数φ的增加和Rf的减小而增大,常数n对于加筋土应力应变响应影响较小。本研究成果可为工程建设提供理论借鉴。

汕头市压力表计量比对结果分析

压力表是工业控制和测量过程中常用的设备,在各行业应用广泛,其准确度对于社会安全和生产工作具有重要意义。根据汕头市市场监督管理局《关于组织开展2022年度计量比对(能力验证)工作的通知要求》,组织开展了汕头市压力表计量比对工作,参比单位为汕头市部分已建标的企业,涉及制药、电力、军工和检测等代表性行业。笔者通过比对数据的汇总及分析,对压力表检定校准过程中的关键问题进行识别,并提出切实可行的解决意见及建议。